class: center, top, .title-slide, title-slide # Biostats Lecture 5:
Statistical Hypothesis Testing ## Public Health 783 ### Ralph Trane ### University of Wisconsin–Madison
### Fall 2019 --- # Recap Random variables Distributions Estimators Estimators are random variables! (for example, the average is a random variable) --- layout: true # Statistical Hypothesis Testing --- **Scenario**: We've been playing a simple game. Everytime you roll a six, I pay you a dollar. Everytime I roll a six, you pay me a dollar. I've had crazy good luck, and by the end of the day won a lot of money from you. -- You accuse me of cheating, and demand to test the dice I've been using! I agree to let you test them, but ONLY if you do it in a sound, statistical manner. How to go about that? -- You decide to roll the dice `\(8\)` times each, for a total of `\(42\)` rolls. You assume they'll all behave the same, so the probability of rolling a six is the same for all three dice. --- **Setup**: Let `\(X_1, X_2, ..., X_{42}\)` be the outcomes of the thirty "trials". Each trial consists of rolling a die, and check if it's a six or not. If it's a six, we'll call it a success, if not we'll call it a failure. I.e. `\(X_i \sim\)` -- `\(\text{Bernoulli}(\pi)\)`. *IF* the dice are fair, `\(P(X_i = 1) = 1/6\)` for all `\(i = 1,2,...,42\)`. *IF* the dice are fair, we would expect to roll a `\(6\)` close to `\(\frac{1}{6}\cdot 42 = 6\)` times, i.e. about `\(5\)` of the `\(X\)`'s should be `\(1\)`'s. What would cause you to reject the idea that the dice are fair? -- If we see way more than `\(6\)` sixes. What would be "way more"? `\(7\)`? `\(8\)`? `\(17\)`? --- In terms of probabilities: what is the *probability* of observing at least `\(10\)` sixes *IF* the `\(P(X_i = 1) = \frac{1}{6}\)`? * if the probability is small, `\(10\)` is a lot of sixes * if the probability is large, `\(10\)` is a reasonable number of sixes First, introduce the random variable `\(Y =\)` number of sixes `\(= X_1 + X_2 + ... X_{42}\)`. The probability of observing more than `\(10\)` sixes is `\(P(Y \ge 10)\)`. To find this, we need the distribution of `\(Y\)`, which is -- `\(\text{Binomial}(42, \pi)\)`, where `\(\pi\)` is the probability of rolling a six. --- *IF* the dice are fair, `\(\pi = \frac{1}{6}\)`. So *IF* the dice are fair, the distribution of `\(Y\)` looks like this: <center>
</center> --- The probability we want to find is the red area below. We will do this in SAS in just a second. The result is 0.07905. <center>
</center> --- This means that *IF* the true probability of rolling a six with these dice is indeed `\(\frac{1}{6}\)`, the probability of rolling `\(10\)` or more sixes is `\(0.07905\)`. This probability is called the *p-value* for the test `\(H_0: \pi = 1/6\)` when testing against `\(H_A: \pi > 1/6\)`. Is this small enough to convince you that the true probability is *NOT* `\(\frac{1}{6}\)`? --- </br> </br> </br> </br> .center[ **In SAS.** ] --- ## Different (but the same) approach Instead of looking at `\(Y\)` (number of sixes), look at the proportion of sixes. I.e. `$$\hat{p} = \frac{Y}{n} = \frac{1}{n}(X_1 + ... + X_{42}) = \frac{1}{n} \sum_{i=1}^{42} X_i$$` This is an average, so CLT tells us it's normally distributed around the true value of `\(\pi\)`, and variance `\(\frac{\text{Var}(X_i)}{n} = \frac{\pi(1-\pi)}{n}\)`. We reject the idea that the true value of `\(\pi\)` is `\(\frac{1}{6}\)` when `\(\hat{p}\)` is "far from" `\(\frac{1}{6}\)`. I.e. when `\(\hat{p} - \frac{1}{6}\)` is large. When this is large, so is `\(Z = \frac{\hat{p}-1/6}{\text{SD}(\hat{p})}\)`. If we pretend `\(\pi = \frac{1}{6}\)`, then `\(Z \sim N(0,1)\)`! If we pretend `\(\pi = \frac{1}{6}\)`, then `\(\text{SD}(\hat{p}) = \sqrt{\text{Var}(\hat{p})} = \sqrt{\frac{1/6 \cdot (1-1/6)}{42}}\)`, and so we can actually calculate `\(z_{obs}\)`, the observed value of `\(Z\)`. --- ## Different (but the same) approach So, `\begin{align*} \text{p-value} &= P(\hat{p} > p_{obs}) \\ &= P\left(\frac{\hat{p} - 1/6}{\text{SD}(\hat{p})} > \frac{p_{obs} - 1/6}{\sqrt{1/6 \cdot (1-1/6)/42}} \right) &= P(Z > 1.24212) \end{align*}` --- So we found our p-value as the area depicted below. Turns out, this is 0.1071. <img 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" width="450" height="300" style="display: block; margin: auto;" /> This strategy can be used every time we the quantity of interest in follows a (at least approximately) normal distribution. Subtract the mean and divide by the standard deviation to get the standard normal. Then find the probability. --- ## Group Comparison Two groups, 15 observations in each group. Want to test `\(H_0: \mu_X = \mu_Y\)` against `\(H_A: \mu_X \neq \mu_Y\)`. <img 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" width="450" height="300" style="display: block; margin: auto;" /> --- Natural to look at `\(\bar{X} - \bar{Y}\)`. If `\(n\)` is "large enough", both of these quantities are normally distributed. From last week, normal minus normal is normal. So `\(\bar{X} - \bar{Y}\)` is normal! Next question: exactly what normal would it be *IF* we pretend the null hypothesis is true? Mean: `\(E(\bar{X} - \bar{Y}) = E(\bar{X}) - E(\bar{Y})=\)` -- `\(\mu_X - \mu_Y =\)` -- `\(0\)` Variance (assuming independence): `\(\text{Var}(\bar{X} - \bar{Y}) =\)` -- `\(\text{Var}(\bar{X}) + \text{Var}(\bar{Y}) = \frac{\sigma_X^2}{n_X} + \frac{\sigma_Y^2}{n_Y}\)`. So `\(Z = \frac{\bar{X} - \bar{Y}}{\text{SD}(\bar{X} - \bar{Y})} = \frac{\bar{X} - \bar{Y}}{\sqrt{\text{Var}(\bar{X} - \bar{Y})}} \sim N(0,1)\)`. What's the problem here? -- We don't know `\(\sigma_X^2\)` or `\(\sigma_Y^2\)`! --- Luckily, we can simply *estimate* both, and plug them in. When we do this, the result no longer follows a standard normal distribution... -- BUT it follows a particular `\(t\)`-distribution. How to calculate the exact degrees of freedom is a bit tricky, but it can be done. **For the patient type:** The degrees of freedom is `\begin{align*} \text{df} &= n_X + n_Y - 2 \end{align*}` if we are willing to assume `\(\sigma_X^2 = \sigma_Y^2\)`. In this case we would use `\(s_X^2 = s_Y^2 = \frac{1}{n_X + n_Y - 2}\left(\sum_{i=1}^{n_X} (x_i - \bar{x})^2 + \sum_{i=1}^{n_Y} (y_i - \bar{y})^2\right)\)`. --- If you're not willing to assume `\(\sigma_X^2 = \sigma_Y^2\)`, the degrees of freedom is `\begin{align*} \text{df} &= \frac{\left[\frac{s_X^2}{n_X} + \frac{s_Y^2}{n_Y}\right]^2}{\frac{(s_X^2/n_X)^2}{n_X - 1} + \frac{(s_Y^2/n_Y)^2}{n_Y - 1}}, \end{align*}` and we would then use the regular sample variances as estimates: `\begin{align*} s_X^2 &= \frac{1}{n_X - 1} \sum_{i=1}^{n_X} (x_i - \bar{x})^2 \\ &\\ s_Y^2 &= \frac{1}{n_Y - 1} \sum_{i=1}^{n_Y} (y_i - \bar{y})^2 \end{align*}` --- **For the not so patient type:** Don't worry about it, you'll use software to calculate this. HOWEVER, you will need to know WHEN you can assume equal variance.